The product of two numbers is 5, if their sum is 9/2. What are the numbers? with detail explaniation

Answers

Answer 1

Answer: The numbers are 2 and 2.5

Explanation:

Let one number be "x" and another "y", Note: 9/2 = 4.5 [in decimal form]

[tex]\rule{185}{2}[/tex]

Their product :

[tex]\hookrightarrow \sf x \ \cdot \ y = 5[/tex]    

[tex]\hookrightarrow \sf x = \dfrac{5}{y} \quad \ \ \leftarrow \quad equation _1[/tex]

Their sum :

[tex]\hookrightarrow \sf x + y = 4.5[/tex]

[tex]\hookrightarrow \sf x = 4.5-y \quad \ \ \leftarrow \ equation_2[/tex]

Solve them simultaneously:

[tex]\rightarrow \sf 4.5 - y = \dfrac{5}{y}[/tex]

cross multiply

[tex]\rightarrow \sf y(4.5 - y) = 5[/tex]

distribute inside parenthesis

[tex]\rightarrow \sf -y^2 +4.5y - 5 = 0[/tex]

multiply by -1

[tex]\rightarrow \sf y^2 -4.5y + 5 = 0[/tex]

factor them out

[tex]\rightarrow \sf ( y - 2.5)(y - 2)= 0[/tex]

set to 0

[tex]\rightarrow \sf y = 2.5, \ 2[/tex]

Another number:

When one number is 2.5, then another: 4.5 - 2.5 = 2

When one number is 2, then another: 4.5 - 2 = 2.5

Hence, the numbers are 2.5 and 2

Check:

Product: 2 × 2.5 = 5Sum: 2 + 2.5 = 4.5 or 9/2
Answer 2

The numbers obtained by the given condition that the product of two numbers is 5 if their sum is 9/2 will be x =( 2 or 5/2) and y = ( 2 or 5/2).

How to form an equation?

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let's say the first number is x and the second is y then

Product xy =  5

Sum x + y = 9/2

substitute y = 9/2 - x into first

x( 9/2 - x) = 5

2x² - 9x + 10 = 0

2x² -5x -4x + 10 = 0

x( 2x - 5 ) -2( 2x -5 ) = 0

(x -2)(2x -5) = 0

x =2 and x = 5/2

Corresponding to x y will be y = 2 and y = 5/2.

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Related Questions

Wendy winholtz 8 year savings certificate pays an annual interest rate of 5.3% at the end of 5 years she cashed out the 6,000 CD and paid a penalty of 12 month simple interest. What penalty did she pay

Answers

Answer:

  318

Step-by-step explanation:

The rate of 5.3% is an annual rate, and specifies the amount of interest earned in a 12-month period by the principal amount of the CD. The interest amount is found by multiplying the interest rate by the principal amount.

__

penalty

The amount of the penalty is 5.3% of 6000:

  0.053 × 6000 = 318

Wendy paid a penalty of 318 for her early withdrawal.

solve the equation
x + 10 = 20

Answers

20-10=10 therefore X=10

10+10=20

In ΔABC, m∠A = 2m∠B and m∠B = 3m∠C.
What is m∠C?

Answers

A triangle is a three-edged polygon with three vertices. The measure of ∠C is 18°.

What is a triangle?

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

Let the measure of ∠C be represented by x. Given the measure of ∠A= 2(∠B), while the measure of ∠B=3(∠C). Therefore, the measure of angles can be written as,

∠A = 2(∠B) = 2[3(∠C)] = 6x

∠B = 3x

∠C = x

Now, since the sum of all the angles of a triangle is 180°. Therefore,

∠A + ∠B + ∠C = 180°

6x + 3x + x = 180°

10x = 180°

x = 18°

Hence, the measure of ∠C is 18°.

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You plan to build a house that is 1 ½ times as long as it is wide. You want the land around the house to be 20 feet wider than the width of the house, and twice as long as the length of the house, as shown at the right.

Answers

The total area with land based on the information given is 3x² + 60x.

How to find the area?

Let the width = x

Let the length = (1.5 × x) = 1.5x

Area = 1.5x × x = 1.5x²

The area along with land:

Width = x + 20

Length = 3 × x = 3x

The total area with land:

= Length × Width

= 3x(x + 20)

= 3x² + 60x.

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Explain a time in your life you underwent metamorphosis

Answers

Answer: Maybe when you Grew from a Baby to a toddler because that would be you growing over time

Step-by-step explanation:

I Hope This Helps!

A rubber bouncy ball is dropped from a
height of 101.00 inches onto a hard flat
floor. After each bounce, the ball returns
to a height that is 19% less than the
previous maximum height. What is the
maximum height reached after the 5th
bounce?

Answers

Using a geometric sequence, it is found that the maximum height reached after the 5th bounce is of 43.48 feet.

What is a geometric sequence?

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

In this problem, the ball is dropped from a height of 101.00 inches onto a hard flat floor, and after each bounce, the height is 19% less, that is, 81% of the previous height, hence the first term and the common ratio are given by:

[tex]a_1 = 101, q = 0.81[/tex]

Then, the height of the nth bounce is given by:

[tex]a_n = 101(0.81)^{n-1}[/tex]

And the height of the 5th bounce is:

[tex]a_5 = 101(0.81)^{5-1} = 43.48[/tex]

The maximum height reached after the 5th bounce is of 43.48 feet.

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A copy machine makes 36 coples per minute. How many coples does it make in 4 minutes and 45 seconds?

Answers

It should make 8, so letter B

A certain city in Washington has a population of 46,400 people.
If the city is 580 sq mi in area, approximately how many people live in each square mile?

Answers

Step-by-step explanation:

please can you divide it will give you the answer

Q5. Find each value.

Answers

Answer:

[tex]a. {( \sqrt{36} )}^{2} = 36[/tex]

[tex]b. ({ \sqrt{ \frac{25}{81} } })^{2} = \frac{25}{81} = 0.3086[/tex]

[tex]c. {( \sqrt{1.99} )}^{2} = 1.99[/tex]

[tex]d. {( \sqrt{x} })^{2} = x[/tex]

The square exponent is removed with the root .


Estimate the solution to the following system of equations by graphing.
3x + 5y = 14
6x - 4y = 9

Answers

Answer:

(2.405, 1.537)

Step-by-step explanation:

When you graph these, they intersect at (2.405, 1.537).

You can use desmos as a graphing calculator, it is extremely helpful.

Hope this helps!

100 points
1942 divded by 2^4

Answers

Answer: 121.375

Step-by-step explanation:

[tex]2^4=16[/tex]

[tex]\frac{1942}{2^4}[/tex]

[tex]\frac{1942}{16}=121.375[/tex]

A line intersects the points (-5, 1) and (-2,7). What is the slope of the line in simplest form? m=[?}

Answers

Step-by-step explanation:

To find slope : y2- y1 / x2 - x1

we have ( -5 , 1 ) which is ( x1 , y1 )

and ( -2 , 7 ) is ( x2 , y2 )

so; 7 - 1 / -2 - (-5)

6/3

= 2

The constant is four

Answers

x=4

Step-by-step explanation:

4x=16y

x=16divide4

x=4

Answer:

y = 4x

Step-by-step explanation:

Take a pair of coordinates, like

(8,32) ; (4,16)

m = (Δy):(Δx)

   = (32-16) : (8 - 4) = 4

y = mx + c

  = 4x +c

Now substitute the values from one of the 2 coordinates' pair.

16 = 16 + c

c = 0

Therefore,

y = 4x

5 more than n is the quotient of n and 4

Answers

Answer:

3

Step-by-step explanation:

Simplify the following: 9 – 2(x - 5) = x + 10

Answers

Answer:

x = 3

Step-by-step explanation:

Hello!

We can distribute the parenthesis and solve for x.

Solve9 - 2(x - 5) = x + 109 - 2x + 10 = x + 1019 - 10 = 3x9 = 3xx = 3

The value of x is 3.

We can plug it back in to check if it works.

Check9 - 2(x - 5) = x + 109 - 2(3 - 5) = 3 + 109 - 2(-2) = 3 + 109 + 4 = 3 + 1013 = 13

Correct!

Answer:

[tex]\huge\boxed{\sf x = 3}[/tex]

Step-by-step explanation:

Given equation:

9 - 2(x - 5) = x + 10

Distribute

9 - 2x + 10 = x + 10

Subtract 10 to both sides

9 - 2x = x

Add 2x to both sides

9 = x + 2x

9 = 3x

Divide 3 to both sides

9/3 = 3x/3

3 = x

OR

x = 3

[tex]\rule[225]{225}{2}[/tex]

There are 35 students on the Step Team to raise a total of 3,500 for uniforms. So far they have raised a total of 1,800. How much more money in dollars, does each member of the Step Team need to raise

Answers

Answer:

48.57 USD

Step-by-step explanation:

Just subtract 3500 from 1800 you get 1700

then

1700 divided by 35

Statistics

Assume there are 20 advanced English level students, 8 intermediate English
level students and 15 beginner English level students at statistics class. What
is the probability of selecting 10 advanced English level students and 10
non_ advanced English level students?

Answers

Answer:

no thank you sorry 4h he'll be a great day of school and I have been a while ago but it's a good time 44

Answer:

o

Step-by-step explanation:

Hurry HELP :The net of a solid figure is shown below: Four squares are shown side by side in a row. The second square has a square above it and a square below it. All the squares have side lengths equal to 5 inches Which calculation will give the total surface area of the solid figure? (1 point) a 5 ⋅ 6 ⋅ 6 square inches b 6 ⋅ 5 ⋅ 5 square inches c 6 ⋅ 5 ⋅ 5 ⋅ 5 square inches d 5 ⋅ 6 ⋅ 6 ⋅ 6 square inches

Answers

The calculation that will give us the total surface area of the solid figure that is made up of square faces is: B. 6 × 5 × 5

What is the Area of a Square?

Area of a square = (side length)².

Therefore are six (6) square faces that make up the solid figure.

Area of the 6 square faces = total surface area of the solid figure = 6(5²)

Total surface area of the solid figure = 6 × 5 × 5

Total surface area of the solid figure is: B. 6 × 5 × 5

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simplify 2 2/3-1.25+5/6

Answers

Answer:

2.25or21/4

Step-by-step explanation:

hope it helps

Answer:

2 1/4 or 2.25

Step-by-step explanation:

Given

Expression:

2 2/3 - 1.25 + 5/6

Solution

Simplify it in below steps:

2 2/3 - 1.25 + 5/6 = 2 + 2/3 - 1 - 0.25 + 5/6 = 1 + 4/6 + 5/6 - 1/4 =1 + 9/6 - 1/4 =1 + 1 + 3/6 - 1/4 = 2 + 2/4 - 1/4 = 2 + 1/4 = 2 1/4 or 2.25

What is the value of 9+n/3when n equals 12

Answers

Answer:

13

Step-by-step explanation:

Divide 12 by 3 first because of (PEMDAS) you get 4 tge add that to the 9 the you get 13.

P = parentheses

E = exponent

M = multiplication

D = division

A = addition

S = subtraction

solving separable differential equation DY over DX equals xy+3x-y-3/xy-2x+4y-8​

Answers

It looks like the differential equation is

[tex]\dfrac{dy}{dx} = \dfrac{xy + 3x - y - 3}{xy - 2x + 4y - 8}[/tex]

Factorize the right side by grouping.

[tex]xy + 3x - y - 3 = x (y + 3) - (y + 3) = (x - 1) (y + 3)[/tex]

[tex]xy - 2x + 4y - 8 = x (y - 2) + 4 (y - 2) = (x + 4) (y - 2)[/tex]

Now we can separate variables as

[tex]\dfrac{dy}{dx} = \dfrac{(x-1)(y+3)}{(x+4)(y-2)} \implies \dfrac{y-2}{y+3} \, dy = \dfrac{x-1}{x+4} \, dx[/tex]

Integrate both sides.

[tex]\displaystyle \int \frac{y-2}{y+3} \, dy = \int \frac{x-1}{x+4} \, dx[/tex]

[tex]\displaystyle \int \left(1 - \frac5{y+3}\right) \, dy = \int \left(1 - \frac5{x + 4}\right) \, dx[/tex]

[tex]\implies \boxed{y - 5 \ln|y + 3| = x - 5 \ln|x + 4| + C}[/tex]

You could go on to solve for [tex]y[/tex] explicitly as a function of [tex]x[/tex], but that involves a special function called the "product logarithm" or "Lambert W" function, which is probably beyond your scope.

Complete the table of values for the equation, 16x + 4y = 12.

x y
-2
-1
0
1
2

Answers

The x-y coordinates for the given equation are: (-2,11),(-1,7),(0,3), (1,-1) and (2,-5).

Linear Function

A linear function can be represented by a line. The standard form for this equation is: ax+b , for example, y=2x+7. Where:

a= the slope;b=the constant term that represents the y-intercept.

The given equation is 16x + 4y = 12. For solving this question, you should replace the given values of x  for finding the values of y.

Thus,

For x= -2,  the value of y will be:

       16*(-2)+4y=12

      -32+4y=12

      4y=12+32

     4y=44

      y=11

For x= -1,  the value of y will be:

         16*(-1)+4y=12

-16+4y=124y=12+164y=28y=7For x= 0,  the value of y will be:

         16*(0)+4y=12

0+4y=124y=124y=12y=3For x= 1,  the value of y will be:

         16*(1)+4y=12

16+4y=124y=12-164y=-4y= -1For x= 2,  the value of y will be:

         16*(2)+4y=12

32+4y=124y=12-324y=-20y= -5

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Simplify
Inx + lny + ln3

Answers

Step-by-step explanation:

[tex] ln(x) + ln(y) + ln(3) [/tex]

[tex] ln(3xy) [/tex]

this shape is a triangular Pyramid the 3 sides slant height is 14 the base width is 8 and the base height is 6.9

Answers

The surface area of a triangular prism with the 3 sides slant height as 14 the base width as 8 and the base height as 6.9 is 155. 705 in²

What is the surface area of a triangular prism?

The surface area of a triangular pyramid is the total area of all it's faces.

The properties of a triangular prism are;

It has a triangular base It is bounded y three lateral triangular faces meeting at  one vertex. It has all its faces as triangles

How to determine the surface area

Surface area = Base Area + 1÷2 (perimeter × base height)

But base area = 1÷2 (base side × height)

Base area = 1÷ 2 (8 × 14) = 0.5 × 112 = 56 in²

Perimeter = sum of all the sides = 14 + 8 + 6.9 = 28. 9 in

Base height = 6. 9in

Surface area = 56 + 1 ÷ 2 ( 28.9× 6. 9) = 56 + 0.5 × 199.41 = 56 + 99. 705 = 155. 705 in²

Surface area = 155. 705 in²

Therefore, the surface area of the triangular prism is 155. 705 in²

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If events A and B are independent, what must be true?

P(A|B) = P(B)
P(A|B) = P(A)
P(A) = P(B)
P(A|B) = P(B|A)

Answers

Answer: P(A|B) = P(A)

Step-by-step explanation:

If they are independent, one event being given doesn't impact the probability of the other event.

Answer:b

Step-by-step explanation:

b

The distance between two cities is 13 kilometers. There are approximately 1.6 kilometers in 1 mile. What is the number of miles between the two cities?

Answers

The number of miles between the two cities is 8.13 miles.

What is the number of miles between the two cities?

In order to determine  the number of miles between the two cities, we would have to divide 13 kilometers by 1.6 miles. Division is when a number is grouped into equal numbers using another number.

Number of miles = 13 / 1.6 = 8.13 miles

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Classify the following triangle as acute, obtuse, or right.
A. Obtuse
B. Acute
C. Right
D. None of these

Answers

Answer:

Acute Triangle.

Explanation:

The figure shows an equilateral triangle which has all the angles equal.

Acute Triangles are those who has angles less than 90°

Hence, an equilateral triangle is always an acute triangle.

Additional,

A right angle triangle has 90° angle.

An obtuse triangle has greater than 90° angle.

Jessica and Callista go the local burger joint. They both want to buy the meal deal. Jessica has 34 of the money needed to buy the meal deal and Callista has half of the money needed to buy the meal deal. If the meal deal was $3 cheaper, then together they would have exactly enough money to buy two of the meal deals.

What is the original price of the meal deal? Show or explain how you got your answer.

Answers

The original price of the meal deal if they would have exactly enough money to buy two of the meal deal is $4

How to write and solve equation?

let

x = cost of the meal

Both = 2x - 3

Jessica = 3/4xCallista = 1/2x

3/4x + 1/2x = 2x - 3

(3+2)x / 4 = 2x - 3

5/4x = 2x - 3

5/4x - 2x = - 3

(5-8)x/ 4 = -3

-3/4x = -3

x = -3 ÷ -3/4

= -3 × -4/3

= 12/3

x = $4

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what equation defines a line that intersects the graph of 6x-2y=10 exactly once?

Answers

Any line with a slope different than 3 will intercept the given line only once.

What equation defines a line that intersects the graph?

The answer will be any line that is not parallel (nor the same) to the given line.

Remember two lines are parallel if the lines have the same slope and different y-intercept

In this case, the given linear equation is:

6x - 2y = 10

y = 3x - 5

So the slope is 3 and the y-intercept is -5.

Then, any line with a slope different than 3 will intercept this line only once.

An example can be:

y = 314*x

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Find the inverse, picture below!

Answers

Answer:

[tex]f^{-1}(x) = (x+7)^2[/tex]

Step-by-step explanation:

[tex]y=f(x) = \sqrt x - 7 \\\\\text{Replace x with y and then solve for y:}\\\\~~~~~~~~x= \sqrt y -7\\\\\implies \sqrt y = x+7\\\\\implies y = (x+7)^2\\\\\implies f^{-1}(x) = (x+7)^2[/tex]

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